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A mixed-integer linear programming model for hydro unit commitment considering operation constraint priorities

RENEWABLE ENERGY 2023年第1期204卷 507-520页

作者： Wu, Xinyu Wu, Yiyang Cheng, Xilong Cheng, Chuntian Li, Zehong Wu, Yongqi Dalian Univ Technol Inst Hydropower & Hydroinformat Dalian 116024 Peoples R China Yunhe Henan Informat Technol Co Ltd Zhengzhou 450003 Peoples R China Guizhou Qianyuan Power Co Ltd Guiyang 550002 Peoples R China

Optimizing hydro unit commitment (HUC) has the potential to improve water use efficiency, but should consider complex constraints from power grid, hydropower station and unit operation. When confronted with extreme operating conditions, conflicting constraints cannot be satisfied simultaneously, resulting in no feasible solution. To overcome this drawback, the constraint grading principle is proposed to illustrate how to convert hard constraints into soft constraints and rank them in priority levels. Soft constraints are destroyed according to priority levels from low to high to obtain a feasible solution, simultaneously minimizing the damage degree of soft constraints. Based on the principle, the HUC model considering operation constraint priorities is proposed. When the initial model fails to obtain a feasible solution, low-priority soft constraints are destroyed automati-cally. Finally, the proposed model is linearized to a mixed-integer linear programming (MILP) model. The commercial solver Lingo is adopted to obtain a feasible solution. The modeling results of Guangzhao hydropower station reveal that: The proposed method can effectively solve the problem of no feasible solution due to con-flicting constraints in HUC. Comparing to the penalty function method, the proposed method has better convergence, and strictly reflects the priority of soft constraints.

关键词： Hydro unit commitment Constraint grading mixed -integer linear programming

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A unified framework for bivariate clustering and regression problems via mixed-integer linear programming

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DISCRETE APPLIED MATHEMATICS 2023年 336卷 15-36页

作者： Warwicker, John Alasdair Rebennack, Steffen Karlsruhe Inst Technol KIT Inst Operat Res IOR D-76185 Karlsruhe Baden Wurttembe Germany

Clustering and regression are two of the most important problems in data analysis and machine learning. Recently, mixed-integer linear programs (MILPs) have been presented in the literature to solve these problems. By modelling the problems as MILPs, they are able to be solved very quickly by commercial solvers. In particular, MILPs for bivariate clusterwise linear regression (CLR) and (continuous) piecewise linear regression (PWLR) have recently appeared. These MILP models make use of binary variables and logical implications modelled through big -M constraints. In this paper, we present these models in the context of a unifying MILP framework for bivariate clustering and regression problems. We then present two new formulations within this framework, the first for ordered CLR, and the second for clusterwise piecewise linear regression (CPWLR). The CPWLR problem concerns simultaneously clustering discrete data, while modelling each cluster with a continuous PWL function. Extending upon the framework, we discuss how outlier detection can be implemented within the models, and how specific decomposition methods can be used to find speedups in the runtime. Experimental results show when each model is the most effective.& COPY;2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Clustering Regression mixed -integer linear programming Outlier detection Decomposition Function fitting

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Decentralised multi-grid coupling for energy supply of a hybrid bus depot using mixed-integer linear programming

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SMART ENERGY 2022年 8卷

作者： Roth, Maximilian Franke, Georg Rinderknecht, Stephan Tech Univ Darmstadt Inst Mechatron Syst Mech Engn Otto Berndt Str 2 D-64287 Darmstadt Germany

The present work refers to two current problems in the context of achieving Greenhouse gas (GHG) neutrality: first the curtailment of renewable, volatile power generation units and secondly the high share of the mobility domain in total GHG-emissions. Both problems can be countered by a decentralised, smart energy system that supplies electricity, gas and heat to a hybrid public transport bus fleet and is simultaneously coupled to the public gas grid, public electricity grid and the district heating grid (Multi-Grid-Coupling). The enabling energy conversion unit is a reversible solid oxide cell (rSOC), which is operated in combined heat and power (CHP) mode or in power-to-gas (P2G) mode. P2G is primarily a solution approach for the first-mentioned problem and can thus successively lead to the replacement of fossil energy sources. Furthermore, by integrating industrial waste gases - as a necessary CO2 source for the P2G process - an additional benefit is gained from the CO2 that is emitted anyhow. The hybrid bus fleet constitutes an ecological alternative concept in public transport and therefore addresses the second-mentioned problem. The system, developed under the current state of the art technologies and the current ecological and economic conditions for Europe and Germany, can be operated profitably from the perspective of the system operator. This applies to the economically and ecologically optimised operating schedule of the controllable system elements such as the electrical, thermal and compressed gas storages, rSOC, compressor and the energy exchange with the public grids. To derive the optimal operating schedule of the crosssectoral system, a mixed-integer linear programming (MILP) model is implemented and simulated under the current legal situation.

关键词： Microgrid scheduling mixed -integer linear programming Reversible solid oxide cell Power -to -Gas Combined heat and power Optimisation Operation strategy Clean vehicles directive Renewable energy directive II Sector -coupling Smart energy system Multi -grid -coupling

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Life cycle techno-economic-environmental optimization for capacity design and operation strategy of grid-connected building distributed multi-energy system

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RENEWABLE ENERGY 2024年 230卷

作者： Han, Huizhen Ge, Yongkai Wang, Qingrui Yang, Qing Xing, Lu Ba, Shusong Chen, Guoqian Tian, Tian Chen, Xi Jian, Peiru Huazhong Univ Sci & Technol Sch Energy & Power Engn Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol State Key Lab Coal Combust Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol China EU Inst Clean & Renewable Energy Wuhan 430074 Peoples R China Harvard Univ John A Paulson Sch Engn & Appl Sci Cambridge MA 02138 USA Northumbria Univ Mech & Construct Engn Newcastle Upon Tyne NE1 8ST England Peking Univ HSBC Business Sch Shenzhen 518055 Peoples R China Peking Univ Coll Engn Beijing 100871 Peoples R China MIT Sch Engn 77 Massachusetts Ave Cambridge MA 02138 USA Huazhong Univ Sci & Technol Sch Architecture & Urban Planning Wuhan 430074 Peoples R China Wuhan Opt Valley Environm Protect Technol Co Ltd Wuhan 430205 Peoples R China

Distributed multi-energy systems (DMS) have received increasing attention. Many studies have optimized the capacity and operation strategies of DMS based on multiple objectives, but these studies must discuss the weights of different objectives and have not considered the internal coupling between different objectives. Besides, existing studies have not considered the changes in the actual value of environmental impacts. To address these shortcomings, this paper constructs a technology-economic-environmental optimization model by mixed-integer linear programming. Based on life-cycle assessment, the model quantifies the value of system life-cycle environmental impacts by introducing carbon price. The case results show that the proposed optimization model can reduce the total cost by 28.83 % and the life cycle environmental cost by 3.39 % compared to the traditional model. To reduce the strain on the grid, a new operation pattern (The grid provides fixed electricity to the system throughout the year.) is proposed. The electricity interaction of the system with the grid under the new operation pattern is more than 70 % lower than the system without electricity purchased quantity constraint. Sensitivity analysis shows the total system cost is more sensitive to natural gas and electricity price than carbon price. But carbon price volatility helps reduce system carbon emissions.

关键词： Building distributed multi -energy system Techno-economic-environmental optimization Life cycle assessment mixed -integer linear programming Operation pattern

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Drone routing problem with swarm synchronization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第2期314卷 477-495页

作者： Li, Hongqi Wang, Feilong Zhan, Zhuopeng Beihang Univ Sch Transportat Sci & Engn 37 Xueyuan Rd Beijing 100191 Peoples R China

The advantages of rotary-wing drone (RWD) delivery modes have already been delineated. However, single-unit RWDs do not completely solve real problems in last-mile parcel deliveries because of limited payload capacity and flight endurance. Currently, drone swarm technology is being rapidly developed. An RWD swarm can deliver heavy or multiple packages to customers;therefore, the RWD swarm strategy can address the payload capacity limitation of RWDs. Herein, an RWD delivery mode that involves dynamic swarms of RWDs in addition to singleunit RWDs is explored. The "dynamic" characteristic permits the RWD members in swarms to vary by coupling/ decoupling operations at nodes. From the routing plan perspective, using RWD swarms for last-mile parcel deliveries is challenging;accordingly, we introduce a swarm synchronization mode that involves interactions among RWD routes. We formally define the drone routing problem with swarm synchronization (DRP-SS) and develop a mixed-integer linear programming model, which considers the decision on RWD swarms and multi trips. An adaptive large neighborhood search heuristic with specific operators is proposed. In the computational experiments, both small- and large-scale instances are used to validate the effectiveness of the mathematical formulation and the heuristic. Several managerial insights are obtained regarding the influence of detours, the utilization of RWD swarms, and the benefits of multi trips. The DRP-SS model and solution method can be used to estimate the performance of the selection of RWD swarms in practical situations.

关键词： Routing Drone swarm synchronization Time window mixed -integer linear programming Adaptive large neighborhood search

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Accelerated dual dynamic integer programming applied to short-term power generation scheduling

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2023年 145卷

作者： dos Santos, Kenny Vinente Colonetti, Bruno Finardi, Erlon Cristian Zavala, Victor M. Univ Fed Amazonas Dept Oil & Gas 6200 Gen RodrigoOctavio AvCoroado 1 BR-69080900 Manaus Amazonas Brazil Univ Fed Santa Catarina Dept Elect & Elect Engn BR-88040900 Florianopolis SC Brazil INESC P&D Brasil BR-11055300 Santos SP Brazil Univ Wisconsin Dept Chem & Biol Engn 1415 Engn Dr Madison WI 53706 USA

The short-term generation scheduling (STGS) problem defines which units must operate and how much power they must deliver to satisfy the system demand over a planning horizon of up to two weeks. The problem is typically formulated as a large-scale mixed-integer linear programming problem, where off-the-shelf commercial solvers generally struggle to efficiently solve realistic instances of the STGS, mainly due to the large-scale of these models. Thus, decomposition approaches that break the model into smaller instances that are more easily handled are attractive alternatives to directly employing these solvers. This paper proposes a dual dynamic integer programming (DDiP) framework for solving the STGS problem efficiently. As in the standard DDiP approach, we use a nested Benders decomposition over the time horizon but introduce multiperiod stages and overlap strategies to accelerate the method. Simulations performed on the IEEE-118 system show that the pro-posed approach is significantly faster than standard DDiP and can deliver near-optimal solutions.

关键词： Dual dynamic integer programming Short-term generation scheduling mixed -integer linear programming

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Drone location and vehicle fleet planning with trucks and aerial drones

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期308卷 113-130页

作者： Rave, Alexander Fontaine, Pirmin Kuhn, Heinrich Catholic Univ Eichstatt Ingolstadt Ingolstadt Sch Management Dept Operat Schanz 49 D-85049 Ingolstadt Germany

In the context of parcel delivery, aerial drones have great potential that particularly applies in rural ar-eas. In these areas drones mostly operate faster than trucks. As drones are limited in their payload, a combination of trucks and drones can be beneficial in reducing last-mile delivery costs. There are two different delivery methods that combine truck and drone delivery: trucks and drones collaborating with each other with drones launched from trucks, and trucks and drones serving customers independently of each other with drones launched from microdepots or the central distribution *** develop a tactical planning model that decides on the cost-optimal vehicle fleet and the location of dedicated drone stations of a logistics service provider that minimizes total costs. The problem setting is modeled as a mixed-integer linear program that allows the assessment of benefits of different transport concepts as well as the impact of mixing different delivery modes. To solve larger instances we develop a specialized adaptive large neighborhood *** present a numerical study for parcel delivery in a rural area where customers live in scattered settlements, e.g., villages or hamlets. The case study shows that it is best to launch drones both from trucks and dedicated drone stations in 58% of all scenarios considered. This fleet mix leads to average cost savings of 33 . 3% compared to an only truck scenario and 14 . 1% if trucks and drones launched from trucks are considered for delivery. Moreover, we find 17 new best-known solutions for benchmark instances from the literature.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Logistics Last -mile delivery Two -echelon location routing problem mixed -integer linear programming Adaptive large neighborhood search

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Two-stage distributionally robust integrated scheduling of oxygen distribution and steelmaking-continuous casting in steel enterprises

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APPLIED ENERGY 2023年 351卷

作者： Zhang, Liu Zhang, Kaitian Zheng, Zhong Chai, Yi Lian, Xiaoyuan Zhang, Kai Xu, Zhaojun Chen, Sujun Chongqing Univ Coll Mat Sci & Engn Chongqing 400000 Peoples R China Chongqing Univ Coll Automat Chongqing 400000 Peoples R China Minist Educ Key Lab Complex Syst Safety & Control Chongqing 400000 Peoples R China Shougang Jingtang United Iron & Steel Co Ltd Minist Energy & Environm Tangshan 063200 Peoples R China

In the steel industry, the imbalance between fluctuating oxygen demand and stable supply generally results in excessive oxygen emissions and power waste. Independent optimal scheduling of oxygen distribution (OD) or steelmaking-continuous casting (SCC) has limited ability to handle this issue. To address this challenge, we propose an integrated scheduling model that allows for flexible interaction between OD and SCC. We first develop an SCC scheduling model that applies to machine sharing of duplex and conventional smelting, and derive an OD scheduling model. A critical demand interface is further designed to connect the scheduling models of SCC and OD, resulting in a mixed integer linear programming-based integrated scheduling model. Existing research overlooks the probability information of demand uncertainty posed by unpredictable interferences, which limits the ability to handle uncertain demands. To address this limitation, we embed demand probability distribution via a data-driven ambiguity set and upgrade the deterministic integrated scheduling model via twostage distributionally robust optimization. Our model was tested with real data and resulted in a 15% reduction in total costs compared to independent scheduling of OD and SCC. Additionally, it effectively reduced uncertainty risk to 8.3% with low conservativeness, demonstrating superior performance compared to recent methods.

关键词： Integrated scheduling Oxygen distribution Steelmaking -continuous casting Distributionally robust optimization mixed -integer linear programming Steel enterprise

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Scheduling quay cranes and shuttle vehicles simultaneously with limited apron buffer capacity

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COMPUTERS & OPERATIONS RESEARCH 2023年 151卷

作者： Yin, Yu-Qi Zhong, Meisu Wen, Xin Ge, Ying-En Shanghai Maritime Univ Sch Econ & Management Shanghai Peoples R China Changan Univ Sch Econ & Management Xian Shaanxi Peoples R China Jiangsu Univ Sci & Technol Sch Econ & Management Zhenjiang Jiangsu Peoples R China Changan Univ Coll Transportat Engn Xian Shaanxi Peoples R China

How to schedule quay cranes (QCs) and shuttle vehicles (SVs) simultaneously or model them in an integrated scheduling problem is one of the most important problems in operations and management of a container terminal. This paper investigates an integrated QC and SV scheduling problem constrained by apron buffer capacity. In this problem, the decisions to make include the bay-to-QC assignment, the QC-bay sequence, the QC-job sequence, the job-to-SV assignment and the SV-job sequence. First, a mixed-integer linear programming model is formulated for this problem to minimize the makespan. Second, the relationships and interactive variables among the four segments of constraints of the proposed model (i.e., scheduling QCs for vessel bays, sequencing jobs handled by a QC in each bay, scheduling SVs for jobs, apron buffer capacity constraints for each vessel bay) are analyzed to present three rules: vessel block rule, near-to-far rule and full-buffer rule. Finally, a sequential insertion algorithm, a greedy insertion algorithm and an improved genetic algorithm are proposed to solve midand large-sized cases for the problem. Numerical experiments show that the algorithms perform well, compared to the off-the-shelf solver. Based on these experiments, managerial implications are discussed for container terminal operations and management.

关键词： Container terminal Quay crane Shuttle vehicle Integrated scheduling problem mixed -integer linear programming Block buffer zone Automated stacking

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The stochastic inventory routing problem on electric roads

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期310卷 156-167页

作者： Gutierrez-Alcoba, Alejandro Rossi, Roberto Martin-Barragan, Belen Embley, Tim Univ Edinburgh Business Sch Edinburgh EH8 9JS Scotland Costain Grp Plc Maidenhead SL6 4UB England

In this work we introduce a green inventory routing problem termed the Stochastic Inventory Routing Problem on Electric Roads (S-IRP-ER), in which a hybrid vehicle navigates a road network with charging opportunities in some road sections, to cover the non-stationary stochastic demand of a single product for a set of retailers in the network. We model the problem using isochrone graphs to represent the real road network. In an isochrone graph nodes are located such that the time to travel any arc is constant all over the network. This allows for tracking the battery level of the vehicle serving retailers, as it charges and discharges continuously while travelling. We formulate a mathematical programming heuristics and prove its effectiveness. We use our model on a realistic instance of the problem, showcasing the different strategies that a vehicle may follow depending on fuel costs in relation to the costs of electricity.(c) 2023 Published by Elsevier B.V.

关键词： Inventory Routing Electric roads Stochastic demand mixed -integer linear programming

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